I couldn't find a the limiting factor... The stars would be dead before we arrived? My best guess. Of course, the qualification would be that we continue to be bound to the speed of light maximum.
This limits our ability to reach galaxies further away from us as they are speeding away faster than we could conceivably travel since our engines would of course be bound by the speed of light.
Some more info: https://www.forbes.com/sites/startswithabang/2016/06/10/can-...
https://en.wikipedia.org/wiki/Andromeda%E2%80%93Milky_Way_co...
[1] https://en.wikipedia.org/wiki/Andromeda%E2%80%93Milky_Way_co...
[2] https://en.wikipedia.org/wiki/Timeline_of_the_far_future#Fut...
Sure, it could take millions of years to cross the galaxy, but we could grow exponentially (like lily pads crossing a pond), at least until other limiting factors kick in.
Also realized, there won't be much "fireworks", since apparently the stars are far enough apart that the merging of two galaxies won't cause much collision.
Still fun to imagine things on that scale, especially in light of some of NASA's beautiful photos of colliding galaxies (like https://www.nasa.gov/image-feature/goddard/2019/hubble-s-daz...).
But when you create space between 2 points they can appear to move faster than the speed of light, despite not actually moving - it's just that there's new space created between them, so the distance between them grows faster than the speed of light.
As an example if you shine a torch at a really far away rock the dot can move faster than c transversally when you wiggle the torch. But the actual light is going at c to the rock and back to you.
PS It is an open question how that does not lead to contradictions when you start considering energy density of the vacuum or the extremely small gravitational waves (which can in principle transmit information) created by the changes in the latter systems. But these effects are astronomically small and it is difficult to imagine even a thought experiment that can detect them.
If you point a laser pointer device to moon from earth (assuming it's a really strong laser), rotating it for a few degrees on earth will result a light mark kms long on moon. The build up time for the mark will even exceed the speed of light if your hand is fast enough. This doesn't mean you broke the law. It just means multiple objects (in this case, each photon hitting the moon) created the illusion of a single object, moving really fast. Background light trying to reach us from the edge of the universe mimics a similar behavior with the added extra spacial dimension. Locations in space aren't objects. They are some points objects can leave marks on. Tracking their speed can always create faster than light situations if you pick a bunch of them conveniently.
Silly ananlogy that absolutely should not be taken too far: imagine somehow shimming an extra micron into every metre here on Earth every second. Or an extra nanometre into every millimetre. Locally, nothing much changes at a scale you can observe, but Los Angeles is moving away from New York City at about 4m/s. And getting faster because we're still shimming extra length into "old metres"; the metre itself hasn't changed, but now there are more of them. If there were something a thousand times farther away from New York than LA, it would be moving at 4km/s and accelerating. A million times farther and it's 4000km/s. A hundred million times farther, and you're at 400,000km/s - but light can't go that fast, so you can't see it as the light can never reach you. Nothing is "moving" (other than the light in this case), but the distances between things is getting bigger nonetheless.
"reach" is possibly the wrong phrase, since it is the corollary of the "observable universe", one might call it the "observing universe", which is the slice of the universe that light from our present day can ever reach due to the accelerating expansion of the universe and the limitation of the speed of light.